Coral Games and the Core of Cores
AbstractCasual observation reveals that groups of people interact on many levels simultane- ously. Examples include political party formation and interaction; the interaction of ¯rms in research consortia; and labor union and confederation formation. In this paper, a model of hierarchical group structures is developed. The model generalizes the existing coalitional theory in several ways and reveals a new connection between characteristic and partition function theories; that they are both valuable components of an overall theory. The stability concept that emerges is called the core of cores. Several results are presented, including necessary and su±cient conditions for the existence of the core of cores and a theorem that demonstrates the relationship between the cores of each level of the organizational structure and the core of cores. The results establish that stability can arise from any combination of stable and unstable components, and suggest a re-thinking of existing coalitional models, taking into account the e®ect of \nearby" games. The framework developed here has immediate applications to various topics in political econ- omy and industrial organization, such as representative voting and corporate mergers.
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Bibliographic InfoPaper provided by American University, Department of Economics in its series Working Papers with number 2008-18.
Length: 32 pages
Date of creation: Sep 2008
Date of revision:
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Web page: http://www.american.edu/cas/economics/
The Core; Complexity in Game Theory; Hierarchies of Groups;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-11-04 (All new papers)
- NEP-CDM-2008-11-04 (Collective Decision-Making)
- NEP-GTH-2008-11-04 (Game Theory)
- NEP-HPE-2008-11-04 (History & Philosophy of Economics)
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